# Basic Math Formulas

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Basic math formulas are the simple formulas which are used in solving different mathematical questions. In mathematics there are various branches such as algebra, calculus, geometry etc. Each branch has its own set of formulas and theories which help in evaluating problems and finding the right solution for the problems. In some questions, more than one formula isused accordingly to find the solution.

Example 1: Find the length of the hypotenuse in the right angle triangle with sides of length 5 cm, 2 cm.

Given are the length of sides of a right angle triangle i.e. 5 cm and 2 cm.
If the triangle ABC has angle C as the right angle;
Then side a = 5 cm; b = 2 cm and c is the hypotenuse.
Pythagorean theorem formula is:c2 = a2 + b2
Therefore c = √(52 + 22) = √(25 + 4) = √29 cm.
Hence, Hypotenuse = √29 cm.

Example 2: Expand the given algebraic expression: (2x + 3y)2

This is an algebraic expression.
The formula that can be used for expansion of the above given type is:
(a + b) 2 = a2 + b2 + 2ab.
Here the given expression is (2 x + 3y) 2
If, a = 2x and b = 3y.
(2x+3y)2 = (2x)2 + (3y)2 + 2(2 x)(3 y).
Hence, (2x + 3y)2= 4x2 + 9y2 + 12xy.
Therefore, (2x + 3y)2 = 4x2 + 9y2 + 12xy.